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Unformatted text preview: Name: Instructions. Show all work in the space provided. Indicate clearly if you continue on the back side, and write your name at the top of the scratch sheet if you will turn it in for grading. No books or notes are allowed, but a scientific calculator is ok  though unnecessary . All work must be shown to receive credit. Please do not give decimal approximations for square roots, for trigonometric or exponential functions, or for . There are 8 problems worth 25 points each. Maximum score = 200 points. 1. Show that the form under the integral sign is exact (meaning that the integral is pathindependent), and evaluate the integral: Z (2 , 4 , 0) (0 , 1 , 1) e x y + z 2 ( dx dy + 2 zdz ) 1 2. Evaluate R S ~ F ~ndA by the divergence theorem, if ~ F = [cos y, sin x, cos z ] and S is the surface of x 2 + y 2 4, 0 z 1. 2 3. Use the power series method to find the general solution to y 3 x 2 y = 0. (That is, find the general solution y = k =0 a...
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 Summer '08
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